Homogeneous ignition for a three-step chain-branching reaction model

Abstract

Spatially homogeneous thermal explosions governed by a three-step chain-branching kinetic model are described in the asymptotic limit of large activation energy for a range of chain-branching cross-over temperatures. The model consists of a sequence of chain-initiation, chain-branching and chain-termination steps. Temperature-sensitive Arrhenius kinetics is employed for the initiation and branching steps, while the termination step has a temperature-independent rate. Marked distinctions in structure arise as the magnitude of the chain-branching cross-over temperature is increased relative to the initial system temperature. Attention is focused on the regime where the chain-branching cross-over temperature is close to the initial system temperature. Results are also obtained for the fast and slow explosion limits where the two temperatures are not close.